1) Popular opinion is the greatest lie in the world.
This aphorism basically means that the world is full of lies. It infers that lying is common in the world.

2) The surest way to be deceived is to consider oneself cleverer than others.
This aphorism means that over-estimating yourself will get one into trouble. It infers that people should be modest and never think yourself better than others.

3) Among even the happiest married couples there are always moments of regret
This aphorism means that no matter how happy one might seem to be, one is always likely to have regrets. It infers that people are always not satisfied and will feel regretful atone point about his/her decision.